Abstract
The first part of the paper deals with the model of minimal coupling of an Abelian Chern-Simons gauge field with some matter current. The elements of exterior calculus are used to solve the gauge field equations of motion under transversal, Weyl, and Coulomb gauges. The second part reviews the model proposed by G. Semenoff (a scalar matter field couples with a topologically massive gauge field). It is shown that the qdeformed permutation algebra arises both in transversal and Weyl gauges. In this case, the following alternative exists: either the model admits only a Bose-Fermi transmutation in a non-simply connected region, or an anyonic-type matter field is admissible when the consideration is restricted by some contractible subset of a punctured plane. Bibliography: 16 titles.
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